crosstabulation.Rmd

---
title: 'Crosstabulation'
---

```{r, include=FALSE, message=F}
library(tidyverse)
library(pander)
```

## Crosstabulations and $\chi^2$ {- #crosstabs}

We saw in a previous section
[how to create a frequency table of one or more variables](#frequency-tables).
Using that previous example, assume we already have a crosstabulation of `age`
and `prefers`

```{r, include=F}
lego.duplo.df <- readRDS("data/lego.RDS")
lego.table <- xtabs(~age+prefers, lego.duplo.df)
lego.duplo.df %>% glimpse
```

```{r}
lego.table
```

We can easily run the inferential $\chi^2$ (sometimes spelled "chi", but
pronounced "kai"-squared) test on this table:

```{r}
lego.test <- chisq.test(lego.table)
lego.test
```

Note that we can access each number in this output individually because the
`chisq.test` function returns a list. We do this by using the `$` syntax:

```{r}
# access the chi2 value alone
lego.test$statistic
```

Even nicer, you can use an R package to write up your results for you in APA
format!

```{r}
library(apa)
apa(lego.test, print_n=T)
```

[See more on automatically displaying statistics in APA format](#apa-output)

### Three-way tables {-}

You can also use `table()` or `xtabs()` to get 3-way tables of frequencies
(`xtabs` is probably better for this than `table`).

For example, using the `mtcars` dataset we create a 3-way table, and then
convert the result to a dataframe. This means we can print the table nicely in
RMarkdown using the `pander.table()` function, or process it further (e.g. by
[sorting](#sorting) or [reshaping](#reshaping) it).

```{r}
xtabs(~am+gear+cyl, mtcars) %>%
  as_data_frame() %>%
  pander()
```

Often, you will want to present a table in a wider format than this, to aid
comparisons between categories. For example, we might want our table to make it
easy to compare between US and non-US cars for each different number of
cylinders:

```{r}
xtabs(~am+gear+cyl, mtcars) %>%
  as_data_frame() %>%
  reshape2::dcast(am+gear~paste(cyl, "Cylinders")) %>%
  pander()
```

Or our primary question might be related to the effect of `am`, in which case we
might prefer to incude separate columns for US and non-US cars:

```{r}
xtabs(~am+gear+cyl, mtcars) %>%
  as_data_frame() %>%
  reshape2::dcast(gear+cyl~paste0("US=", am)) %>%
  pander()
```